OFFSET
1,2
COMMENTS
a(n) is the circumference of the n X n X n grid graph for n > 1.
LINKS
Eric Weisstein's World of Mathematics, Graph Circumference
Eric Weisstein's World of Mathematics, Grid Graph
Index entries for linear recurrences with constant coefficients, signature (3, -2, -2, 3, -1).
FORMULA
a(n) = (2 n^3 + (-1)^n - 1)/2.
a(n) = 3*a(n-1) - 2*a(n-2) - 2*a(n-3) + 3*a(n-4) - a(n-5).
G.f.: 2*x^2*(4 + x + x^2)/((-1 + x)^4*(1 + x)).
MAPLE
seq(n^3-modp(n, 2), n=1..50); # Muniru A Asiru, Mar 25 2018
MATHEMATICA
Table[n^3 - Mod[n, 2], {n, 20}]
Table[(2 n^3 + (-1)^n - 1)/2, {n, 20}]
LinearRecurrence[{3, -2, -2, 3, -1}, {0, 8, 26, 64, 124}, 20]
CoefficientList[Series[2 x (4 + x + x^2)/((-1 + x)^4 (1 + x)), {x, 0, 20}], x]
PROG
(GAP) List([1..50], n->n^3- n mod 2); # Muniru A Asiru, Mar 25 2018
(PARI) a(n) = n^3 - (n%2); \\ Altug Alkan, Mar 25 2018
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Eric W. Weisstein, Mar 25 2018
STATUS
approved